# Approximate Distributions of Order Statistics

## With Applications to Nonparametric Statistics

• R.-D. Reiss
Book

Part of the Springer Series in Statistics book series (SSS)

1. Front Matter
Pages i-xii
2. ### Introduction

1. R.-D. Reiss
Pages 1-8
3. ### Exact Distributions and Basic Tools

1. Front Matter
Pages 9-9
2. R.-D. Reiss
Pages 11-63
3. R.-D. Reiss
Pages 64-82
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Pages 83-104
4. ### Asymptotic Theory

1. Front Matter
Pages 105-105
2. R.-D. Reiss
Pages 107-150
3. R.-D. Reiss
Pages 151-205
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Pages 206-228
5. R.-D. Reiss
Pages 229-239
5. ### Statistical Models and Procedures

1. Front Matter
Pages 241-241
2. R.-D. Reiss
Pages 243-271
3. R.-D. Reiss
Pages 272-291
4. R.-D. Reiss
Pages 292-317
6. Back Matter
Pages 318-355

### Introduction

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern­ ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi­ mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima­ tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

### Keywords

Mathematica Parametric statistics Random variable probability statistical theory statistics

#### Authors and affiliations

• R.-D. Reiss
• 1
1. 1.Fachbereich 6, MathematikUniversität Gesamthochschule SiegenSiegenFederal Republic of Germany

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4613-9620-8
• Copyright Information Springer-Verlag New York 1989
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4613-9622-2
• Online ISBN 978-1-4613-9620-8
• Series Print ISSN 0172-7397
• Buy this book on publisher's site